The effectiveness of big-M modeling relies on the tightness of coefficient bounds as otherwise the linear relaxations are too weak to efficiently prune the branch-and-bound tree. [1]} derive a number of ways to obtain such bounds, however these approaches can add significant overhead to the solution times, and don't generalize well in the presence of arbitrary constraints. This motivates a nonlinear approach which circumvents the need to calculate these \(2D\)  different bounds. [1]} also proposed adding the cardinality constraint via type-1 specially ordered sets (SOS-1) [3]}. An SOS-1 constraint on a set of variables enforces that no more than one variable within the set is nonzero. In this case
\((1-z_i)\xi _i = 0 \iff \lbrace \xi _i, 1 - z_i\rbrace  : \text{SOS-1}\) 
